Class ${}_1$ has data points $\{1,2,3\}$ while $\{-5,-3,-2\}$ belong to class ${}_2.$

a$)$ What are the augmented vectors?

b$)$ Show the solution region in the weight space.

c$)$ Starting with zero initial weights and using single sample perceptron algorithm, obtain a linear discriminant function that separates the two classes. Let $=1.$